Sorry for the delay in seeing this post! Hopefully the flowing information will be of some use to you, or anyone else who searches for similar info.
Big thanks to @Brent and @SGS for referencing GameSparks in this post
@byron5
With GameSparks we can hopefully get your turn-based game up and running!
You can pick up our SDK with a handy guide on how to install it from here: https://docs.gamesparks.com/sdk-center/
As @SGS mentioned you can follow this tutorial on how to set up GameSparks with Corona: https://docs.gamesparks.com/getting-started/creating-a-game/corona-setup.html
Here is another tutorial on how to create an asynchronous tic tac toe game and some basic matchmaking through GameSparks: https://docs.gamesparks.com/tutorials/game-engine-integrations/corona-1v1-asynchronous-match.html
@ojnab
As for push notifications I think that this tutorial will be of good use to you:
https://docs.gamesparks.com/tutorials/social-features/configuring-firebase-cloud-messaging.html
This tutorial uses Google Firebase and it will guide you on how to get Firebase set up through GameSparks and how to get your game to allow push notifications to be sent to your players on your behalf. Other than that our tic tac toe tutorial is a really good example of how to create a turn based game with a basic matchmaking system.
Also if anyone needs any help regarding GameSparks please feel free to ask in the forums or contact us on our support page!
https://support.gamesparks.net/support/home
Thanks,
Clare